To prepare for his fortune-telling tea party, Teeha brewed a giant pot of tea by tossing teabags into a large cauldron of water. The 100-lb mixture was 99% water by weight. Teeha then boiled the mixture until it was only 98% water by weight. What was the weight of the mixture when it was 98% water by weight?
Answer: Before evaporation there was 1 pound of teabags to 99 pounds of water. Since the teabags did not evaporate, the total weight of the teabags in the mixture after boiling the water remained at 1 pound and the water must have been 49 lbs. which is 2% of the total weight.
To solve the problem with algebra, we could let the weight of the water after boiling be x pounds and then the requirement that the water constitute 98% of the mixture by weight would be written: x/(x+1) = 0.98 from which we obtain x = 49.
